A tube processing machine has a clamping chuck for clamping a tube that is to be processed. The clamping chuck has clamping jaws which are moved by electric, pneumatic or hydraulic actuators in the radial direction of a clamping centre of the clamping chuck from a non-operational position into an operational position in which the clamping jaws clamp a tube arranged between them. Pressure sensors on the clamping jaws serve to regulate the forces exerted on the tube in question by the clamping jaws in the operational position.